A Tool Extracting Summative Profiles From Person Score Profiles

Abstract

Abstract. In this paper a profile analysis that utilizes principal component analysis (PCA) is introduced. Although PCA is popular for a dimension reduction method, it is not well known that unrotated components algebraically are summative profiles which linearly encapsulate person score profiles in a population. The summative profiles include one level summative and several pattern summative profiles. The level summative profile represents the overall ability or achievement, like general ability in factor analysis. The pattern summative profiles characterize prototypical score patterns for individuals and provide us collective information about individuals’ strengths and weaknesses on their score profiles. In addition, significance of coordinates of summative profiles is tested by constructing their bootstrap empirical confidence intervals. To demonstrate utilities of the current profile analysis, male and female summative profiles of mathematics achievement are compared and the results indicate that male students outperform at an advanced grade.